Setting up complex gear physics
I am pretty sure Blender can do this. The physics is far better than most people think. But....you have to be careful.
I will show you the first step, the next steps you can do according to them.
I made it to animate physically the small golden gear with a motor.

Stabilize the gear with this cylinder (rigid body passive)



change small golden gear to rigid body active, shape mesh, margin 0
same to blue gear
plug the motor like this: add an empty like this: the x - direction is important, else the motor won't work



add rigid body constraint to empty like this:



increase the rigid body substeps:


if you start animation with spacebar, the blue gear will rotate, driven by the small golden gear


result here: https://www.youtube.com/watch?v=LsVekqC-Lno&amp;feature=youtu.be
because of your comments...here next steps

copy the passive cylinder from step 1 to the green gear like this:


stabilize the gear by extruding the cylinder on the other side so that the gear won't fall off like this...please don't kill me because i just make it work, but not pretty, i know my modelling is ugly... ;(




set the green and the big golden gear active bodies with shape mesh and margin 0.

copy the empty from 1st motor to the green gear like this:


change the 1st and 2nd object to green cylinder and month gear like this


extrude the tiny cylinder from step 1 until it reaches in the big golden gear like this:



i will delete it, if you want this.
************** UPDATE *****************
ok, i am very sorry, i will give up for now after trying it for hours. Maybe i am just to new to Blender....just experiencing with it only for quite a month now.
I show you how far i came...here is my result: (bit more than before, but not really satisfying): https://youtu.be/GX0CTrZW9YY
I changed lots of values like weight, friction and so on. Of course the result was different in many ways. Most of the time the gears just fell off....I enlarged the motor gears which helped a lot for stability, but if it will work some time, then the &quot;too large&quot; gears will collide with each other. As you can see in the side view there is a lot of instability with the gears, maybe another good idea would be to create counter weights so that the gears have more stability. Just to make them with &quot;no weight&quot; did not help either so...
And here is the blend file:

*** UPDATE 2 ****
Hi Alda, please don't give up animation. I am not sure but maybe the mistake are the gears...I changed them and then i got this perfect result for the very easy case of just two gears, which i never got before. Video link: https://youtu.be/La7cIyaCQi8. If you are able to change the other gears  (the blue with its corresponding gear) that they can run smoothly like mine (blend file: ), i will try again for the &quot;whole&quot; solution. Unfortunately i am not the right guy to build nice and working gears ...
**** UDPDATE 3 ****
After thinking about it again i remembered my physics class. Important is the 2nd law of Newton: https://en.wikipedia.org/wiki/Momentum#Conservation
So in real physics your example cannot work - i think.
My idea with the counter weight was not bad - but not enough.
Newton says, you have to have the same momentum on both sides (simplified), so you have to add a second motor on the other side with the opposite direction so that it is in balance again.
To simplify it, i have just copied the first gear with my modifications of above which smoothly runs, so i knew it worked. I copied the motor, empty and the gear to both sides...and...i just can repeat: Blender is just awesome and seems to know Newton well...it is not perfect (maybe i made still some mistakes, BUT it looks much better now...with just physics in Blender!!!)
new result: https://youtu.be/LtknpY4xGAw
it is not perfect, but it runs at least in the beginning pretty nice...until it fells off...right now, i am not sure why, but it is an improvement anyway.